DEF0181canonicalv1The Physics Quadrant Matrix
2x2 classification of mathematical frameworks by PDE type (elliptic/hyperbolic) and metric type (Archimedean/non-Archimedean). QFT in (H,A), GR locally in (E,A), Category tau in (H,nA). The fourth quadrant (H,nA) is the only quadrant where the Unification Obstruction does not apply.
Payload
The Physics Quadrant Matrix
2x2 classification of mathematical frameworks by PDE type (elliptic/hyperbolic) and metric type (Archimedean/non-Archimedean). QFT in (H,A), GR locally in (E,A), Category tau in (H,nA). The fourth quadrant (H,nA) is the only quadrant where the Unification Obstruction does not apply.
The Physics Quadrant Matrix
Summary
2x2 classification of mathematical frameworks by PDE type (elliptic/hyperbolic) and metric type (Archimedean/non-Archimedean). QFT in (H,A), GR locally in (E,A), Category tau in (H,nA). The fourth quadrant (H,nA) is the only quadrant where the Unification Obstruction does not apply.
Statement
%
\label{def:physics-quadrant-matrix}
The \textbf{Physics Quadrant Matrix}
classifies physical frameworks by two axes:
PDE type (elliptic/hyperbolic)
and metric type (Archimedean/non-Archimedean).
\medskip
\begin{center}
\renewcommand{\arraystretch}{1.5}
\begin{tabular}{@{}l|c|c@{}}
& \textbf{Archimedean} & \textbf{Non-Archimedean} \\
\hline
\textbf{Elliptic}
& GR (curvature, $\varepsilon$-$\delta$)
& (empty) \\
\hline
\textbf{Hyperbolic}
& QFT (wave eq., renormalization)
& Category $\tau$ \\
\end{tabular}
\end{center}
\medskip
\noindent
Quantum Field Theory sits in the (Hyperbolic, Archimedean) quadrant:
its propagation is wave-type
but its renormalization requires $\varepsilon$-$\delta$.
General Relativity sits in the (Elliptic, Archimedean) quadrant:
its curvature requires Laplacian differentiability
but its causal structure is hyperbolic.
Category~$\tau$ sits in the (Hyperbolic, Non-Archimedean) quadrant.
Proof / Justification
This item is definitional. No manuscript proof is required.
Source Context
- Registry source:
book-02.jsonlline 184 - Manuscript source:
2nd-edition/book-ii-categorical-holomorphy/02_mainmatter/part11/ch66-master-trade-off.texlines 384-417
Lean / Formalization Notes
- Formalization:
formalized - Module:
TauLib.BookII.Mirror.PhysicsQuadrant - Name:
PhysicsQuadrant
Dependencies
- Canonical: I.T10, II.D21, II.T19, II.D72
Related Results
Generated by later projection phases.
Related Publications
Generated by later projection phases.
Revision Notes
- 2026-04-24: Initial pilot migration.
Identifiers
Aliases & legacy IDs
II.D73the-physics-quadrant-matrixdef:physics-quadrant-matrixRelease lines
corpus_v3_workingcorpus_v2Relations
Formalized by (1)
Appears in (1)
Downstream uses (computed) (2)
Items in the corpus that reference this one via load-bearing relations. Computed from the full corpus-v3 graph at build time.
Sources
Version & History
Status disclaimer
A Corpus Item page reports the program's current internal record for this item. It does not imply external verification, scientific consensus, or final proof unless explicitly stated. Read it together with its dependencies, formalization status, and the program's overall stance.